The universe is expanding. How do we know this? We measure the spectra of galaxies. Galaxies are made of stars, and thus the spectra of galaxies look very much like those of stars. In particular, the spectra of stars show strong absorption lines, at wavelengths corresponding to transitions of elements in their atmospheres. One sees the same pattern of absorption lines in galaxy spectra, but they are not at the same wavelengths: they are shifted systematically to the red.
The interpretation: the galaxy is moving away from us. The
wavelength 
of light waves from an object moving away from us at
speed v is shifted by an amount:
where c is the speed of light, 
centimeters per second. This
is the Doppler Effect, which also occurs for sound waves (as
written, it is strictly correct only for speeds much less than the
speed of light). Thus the observation that galaxies are redshifted,
implies that they are moving away from us.
Edwin Hubble also measured the distances to galaxies. He used
the Inverse Square Law, which states that the more distant an
object of a given luminosity, the fainter it appears:
Make sure you understand the distinction between luminosity (the total
amount of energy per second an object is giving off; units of ergs/second) and brightness
(the amount of that energy per second that we perceive through our
eyeballs or telescope; units of ergs/second/square centimeter).
Thus if we measure the brightness of a star whose luminosity we know (therein lies a lengthy tale), we can infer its distance. Hubble measured the brightness of stars called Cepheid variables in galaxies to infer their distances.
He then compared the galaxy distances he measured to their
redshifts. He found that the larger the distance r, the larger the
redshift z (or equivalently, the recession speed v that one infers from
the Doppler formula above):
where 
, the Hubble Constant, is approximately:
(A Megaparsec, or 
parsecs, is a measure of distance. The
nearest big galaxies to our own are a bit less than one Megaparsec
away. One parsec is 3.26 light years, so one Megaparsec is about 
centimeters).
Thus, the galaxies are all moving away from us; the further they are from us, the faster they are moving. This is what one expects if all the galaxies were very close together at one point in time, and went flying apart in what we now call The Big Bang.
Consider two galaxies separated by a distance r; the Hubble Law
says that they are moving apart at a speed 
. So how long
ago were the two galaxies together? Just the time it takes to
travel a distance r at that speed:
One of the properties of an expanding gas is that it cools. The
universe is expanding, therefore it was much hotter in the past.
Indeed, the early universe was extremely hot and extremely dense (but
not extremely small; that's another story). Indeed it was so hot and
dense early on that galaxies couldn't exist, nor could stars or
planets... If you turn the clock back far enough, neither could
molecules or neutral atoms. About one minute after the Big Bang, the
temperature was about 
degrees; the constituents of the universe
consisted of electrons, protons, neutrons, photons (particles of
light), neutrinos, and whatever it is that makes up the dark matter.
And that's it. As the universe cooled and expanded, the neutrons and
protons came together to make several atomic nuclei in a process
called primordial nucleosynthesis, in particular:
, Deuterium: One proton and one neutron (an isotope of hydrogen);
, Helium-3 nuclei: Two protons and one neutron;
, Helium-4 nuclei: Two protons and two neutrons (this is
the most abundant isotope of helium today);
, Lithium-7 nuclei: Three protons and four neutrons, and
of course,
Astronomers have done detailed calculations of the amounts of these various elements that should have been produced in the first minutes after the Big Bang. They conclude that:
;
;
.
An ordinary atom consists of an atomic nucleus, with electrons in orbitals around it. It was much too hot for the nuclei to hold onto their electrons in the early universe, so the atoms were all ionized. Indeed, the universe had to cool down to a temperature of 3000 K before electrons and nuclei could stick together, and neutral atoms could form. This happened roughly 400,000 years after the Big Bang.
The ionized gas, or plasma of the early universe acted as a sort of fog; photons could not travel very far before being deflected. But when neutral atoms formed when the electrons and nuclei came together, the photons were free to travel straight. Thus the Big Bang model predicts that there should be photons arriving at the Earth right now that were ``set free'' 400,000 years after the Big Bang. The detection of these photons in 1965 (the Cosmic Microwave Background) was the defining moment at which the astronomical community became convinced that the Big Bang model was correct. The detailed properties of these photons: their spectrum, their uniformity across the sky, and so on, are in excellent accord with the Big Bang model. (The details of that statement are worth an entire course in itself!).
Our interpretation of the expansion of the universe implies an age of 14 billion years. It turns out that we can also infer the ages of clusters of stars. As stars age, stars of ever lower mass burn out, so in a cluster of stars of a certain age, all the stars more massive than a certain mass will have died out. The oldest clusters are thereby inferred to have an age of about 13 billion years, in excellent agreement with (and reassuringly slightly smaller than) the age inferred from the expansion rate of the universe.
Light travels at centimeters per second: fast,
but not infinitely so. When we see a galaxy at a distance of a few
million light years, those photons left the galaxy a few million
years ago. Thus in astronomy, looking at great distances is looking
back in time. Therefore, we are seeing the most distant galaxies in
our telescopes at a time when they were appreciably younger than the
galaxies we see nearby. Astronomers are currently testing the Big
Bang model further by checking these ideas: do distant galaxies
really look younger than those today? The way galaxies evolve with
time is poorly understood, so it is not completely obvious what we
would look for as signs of youth, but the basic answer to this
question is yes.
Michael Strauss